A dynamical model of remote-control model cars

Simple experiments for which differential equations cannot be solved analytically can be addressed using an effective model that satisfactorily reproduces the experimental data. In this work, the one-dimensional kinematics of a remote-control model (toy) car was studied experimentally and its dynamical equation modelled. In the experiment, maximum power was applied to the car, initially at rest, until it reached its terminal velocity. Digital video recording was used to obtain the relevant kinematic variables that enabled to plot trajectories in the phase space. A dynamical equation of motion was proposed in which the overall frictional force was modelled as an effective force proportional to the velocity raised to the power of a real number. Since such an equation could not be solved analytically, a dynamical model was developed and the system parameters were calculated by non-linear fitting. Finally, the resulting values were substituted in the motion equation and the numerical results thus obtained were compared with the experimental data, corroborating the accuracy of the model.Comment: 5 pages, 9 figure

Dynamics Days Latin America and the Caribbean 2018

This book contains various works presented at the Dynamics Days Latin America and the Caribbean (DDays LAC) 2018. Since its beginnings, a key goal of the DDays LAC has been to promote cross-fertilization of ideas from different areas within nonlinear dynamics. On this occasion, the contributions range from experimental to theoretical research, including (but not limited to) chaos, control theory, synchronization, statistical physics, stochastic processes, complex systems and networks, nonlinear time-series analysis, computational methods, fluid dynamics, nonlinear waves, pattern formation, population dynamics, ecological modeling, neural dynamics, and systems biology. The interested reader will find this book to be a useful reference in identifying ground-breaking problems in Physics, Mathematics, Engineering, and Interdisciplinary Sciences, with innovative models and methods that provide insightful solutions. This book is a must-read for anyone looking for new developments of Applied Mathematics and Physics in connection with complex systems, synchronization, neural dynamics, fluid dynamics, ecological networks, and epidemics

An experiment to address conceptual difficulties in slipping and rolling problems

A bicycle wheel that was initially spinning freely was placed in contact with a rough surface and a digital film was made of its motion. Using Tracker software for video analysis, we obtained the velocity vectors for several points on the wheel, in the frame of reference of the laboratory as well as in a relative frame of reference having as its origin the wheel’s center of mass. The velocity of the wheel’s point of contact with the floor was also determined obtaining then a complete picture of the kinematic state of the wheel in both frames of reference. An empirical approach of this sort to problems in mechanics can contribute to overcoming the considerable difficulties they entail

Video-based analysis of the transition from slipping to rolling

The problem of a disc or cylinder initially rolling with slipping on a surface and subsequently transitioning to rolling without slipping is often cited in textbooks [1-2]. Students struggle to qualitatively understand the difference between kinetic and static frictional forces—i.e., whereas the module of the former is known, that of the latter can only be described in terms of an inequality while the relative velocity at the point(s) of contact is equal to zero. In addition, students have difficulty understanding that frictional forces can act in the direction of motion—i.e., they can accelerate object

Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps

We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported [Phys. Rev. Lett. {\bf 94}, 134102 (2005)] that if $\tau_{ij}$ are random enough the array synchronizes in a spatially homogeneous steady state. Here we study this behavior by comparing the dynamics of a map of an array of $N$ delayed-coupled maps with the dynamics of a map with $N$ self-feedback delayed loops. If $N$ is sufficiently large, the dynamics of a map of the array is similar to the dynamics of a map with self-feedback loops with the same delay times. Several delayed loops stabilize the fixed point, when the delays are not the same; however, the distribution of delays plays a key role: if the delays are all odd a periodic orbit (and not the fixed point) is stabilized. We present a linear stability analysis and apply some mathematical theorems that explain the numerical results.Comment: 14 pages, 13 figures, important changes (title changed, discussion, figures, and references added

Normal coordinates in a system of coupled oscillators and influence of the masses of the springs

Experimental analysis of the motion in a system of two coupled oscillators with arbitrary initial conditions was performed and the normal coordinates were obtained directly. The system consisted of two gliders moving on an air track, joined together by a spring and joined by two other springs to the fixed ends. From the positions of the center of mass and the relative distance, acquired by analysis of the digital video of the experiment, normal coordinates were obtained, and by a non linear fit the normal frequencies were also obtained. It is shown that although the masses of the springs are relatively small compared to that of the gliders, it is necessary to take them into consideration to improve the agreement with the experimental results. This experimental-theoretical proposal is targeted to an undergraduate laboratory

Differences in the attitudes and beliefs about science of students in the physics-mathematics and life sciences areas and their impact on teaching

For this study, we compared the attitudes and beliefs about science of physical science (physics and mathematics) and life science (bio- chemistry and biology) students at the beginning of their university degrees using the CLASS (Colorado Learning Attitudes about Science Survey) tool. It is worth noting that both groups of students received similar physics courses during their high-school education. Through a detailed analysis of the different categories of the test, we examined the differences in performance in each of the areas that make up the questionnaire. Among other aspects, we found that a considerable percentage of life science students (higher than that of physical science students) adopted a novice type of behavior in problem solving. Finally, we discussed the possible causes of the differences found and their implications for teaching